Coupled with the discrete wavelet transform, SPIHT (set partitioning in hierarchical trees) is a highly efficient image compression technique that allows for progressive transmission. One problem, however, is that its decoding can be extremely sensitive to bit errors in the code sequence. In this paper, we address the issue of transmitting SPIHT-encoded images via noisy channels, wherein errors are inevitable. The communication scenario assumed in this paper is that the transmitter cannot get any acknowledgement from the receiver. In our scheme, the original SPIHT code sequence is first segmented into packets. Each packet is classified as either a CP (critical packet) or an RP (refinement packet). For error control, cyclic redundancy check (CRC) is incorporated into each packet. By checking the CRC check sum, the receiver is able to tell whether a packet is correctly received or not. In this way, the noisy channel can be effectively modeled as an erasure channel. For unequal error protection (UEP), each of those packets are repeatedly transmitted for a few times, as determined by a process called diversity allocation (DA). Two DA algorithms are proposed. The first algorithm produces a nearly optimal decoded image (as measured in the expected signal-to-noise ratio). However, its computation cost is extremely high. The second algorithm works in a progressive fashion and is naturally compatible with progressive transmission. Its computation complexity is extremely low. Nonetheless, its decoded image is nearly as good. Experimental results show that the proposed scheme significantly improves the decoded images. They also show that making distinction between CP and RP results in wiser diversity allocation to packets and thus produces higher quality in the decoded images.

An alternative design for constructing multilevel space-time codes is proposed. For a given space-time block code, we combine several component codes in conjunction with set partitioning of the expanded signal constellation according to the coding gain distance criterion. The error performance of an example code is compared with a traditional multilevel space-time code in computer simulation.

We propose a moving picture coding by lapped transform and an edge adaptive deblocking filter to reduce the blocking distortion. We apply subband coding (SBC) with lapped transform (LT) and zero pruning set partitioning in hierarchical trees (zpSPIHT) to encode the difference picture. Effective coding using zpSPIHT was achieved by quantizing and pruning the quantized zeros. The blocking distortion caused by block motion compensated prediction is reduced by an edge adaptive deblocking filter. Since the original edges can be detected precisely at the reference picture, an edge adaptive deblocking filter on the predicted picture is very effective. Experimental results show that blocking distortion has been visually reduced at very low bit rate coding and better PSNRs of about 1.0 dB was achieved.

Embedded zero-tree coding in wavelet domain has drawn a lot of attention for image compression applications. Among noteworthy zero-tree algorithms is the set partitioning in hierarchical trees (SPIHT) algorithm. For images with textures, high frequency wavelet coefficients are likely to become significant after a few scan passes of SPIHT, and therefore the coding results are often insufficient. It is desirable that the low frequency and high frequency components of an image are coded using different strategies. In this paper, we propose a hybrid algorithm using the SPIHT and EBC (embedded block coding) to code low frequency and high frequency wavelet coefficients, respectively; the intermediate coding results of low frequency coefficients are used to facilitate the coding operation of high frequency coefficients. Experimental results show that the coding performance can be significantly improved by the hybrid SPIHT-EBC algorithm.

Set Partitioning in Hierarchical Trees (SPIHT) is a highly efficient technique for compressing Discrete Wavelet Transform (DWT) decomposed images. Though its compression efficiency is a little less famous than Embedded Block Coding with Optimized Truncation (EBCOT) adopted by JPEG2000, SPIHT has a straight forward coding procedure and requires no tables. These make SPIHT a more appropriate algorithm for lower cost hardware implementation. In this paper, a modified SPIHT algorithm is presented. The modifications include a simplification of coefficient scanning process, a 1-D addressing method instead of the original 2-D arrangement of wavelet coefficients, and a fixed memory allocation for the data lists instead of a dynamic allocation approach required in the original SPIHT. Although the distortion is slightly increased, it facilitates an extremely fast throughput and easier hardware implementation. The VLSI implementation demonstrates that the proposed design can encode a CIF (352288) 4:2:0 image sequence with at least 30 frames per second at 100-MHz working frequency.

Let f and g be two maps from a set E into a set F such that f(x) g(x) for every x in E. Sahili [8] has shown that, if min {|f-1(z)|,|g-1(z)|}≤ n for each z∈ F, then E can be partitioned into at most 2n+1 sets E1,..., E2n+1 such that f(Ei)∩ g(Ei)= for each i=1,..., 2n+1. He also asked if 2n+1 is the best possible bound. By using Sahili's formulation of the problem in terms of the chromatic number of line digraphs, we improve the upper bound from 2n+1 to O(log n). We also investigate extended version for more than two maps.

We introduce a differential space-time block code (DSTBC) integrated with trellis coded modulation with two transmit antennas. Our scheme enables transmission of DSTBC encoded symbols as trellis metric rather than concatenating an outer code. Unlike conventional DSTBC, different transmit symbol phase rotations are used for each transmit antenna in order to obtain more options for trellis branch. The set partitioning for proposed codes is derived as well. The decoder computes decision statistic using Viterbi Algorithm with different number of states undergoing Rayleigh fading channels. This approach can provide full diversity gain as well as coding gain simultaneously remaining full transmit rate, which cannot be obtained by conventional DSTBC.

We present an 8-dimensional trellis-coded 8-PSK with a symbol transition constraint that is similar to that of π/4-shift quadrature phase shift keying (QPSK). This scheme can achieve a coding gain of 1.6 to 2.4 dB at the same rate of π/4-shift QPSK on Gaussian channel, and it has also an immunity against the integer multiples of 90 phase ambiguities. In order to label the constellation of the proposed scheme, a constellation partitioning algorithm is presented. This algorithm, on the basis of set partitioning, can be used to label the signal constellation with no coset structure.